• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.285-293
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• 1992

• East Asian mathematical journal
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• v.16 no.2
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• pp.169-174
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• 2000

We give an easy proof that ${\phi}(z)=\frac{z^2_1}{1-z^2_2}$ induces the bounded composition operator $C_{\phi}:\mathcal{B}{\rightarrow}{\bigcap}H^p(B_2)$ defined by $C_{\phi}f=f\;o\;{\phi}$.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.187-195
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• 2009

We investigate the boundary values of the holomorphic mean Lipschitz function. In fact, we prove that the admissible limit exists at every boundary point of the unit ball for the holomorphic mean Lipschitz functions under some assumptions on the Lipschitz order. Moreover, we get embedding theorems of holomorphic mean Lipschitz spaces into Hardy spaces or into the Bloch space on the unit ball in $\mathbb{C}_n$.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.175-192
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• 2004

This talk discusses conditions on the numerical range of a holomorphic function defined on a bounded convex domain in a complex Banach space that imply that the function has a unique fixed point. In particular, extensions of the Earle-Hamilton Theorem are given for such domains. The theorems are applied to obtain a quantitative version of the inverse function theorem for holomorphic functions and a distortion form of Cartan's unique-ness theorem.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.4
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• pp.241-247
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• 2019

A band gap refers to a certain frequency range where the propagation of mechanical waves is prohibited. This work focuses on engineering three-dimensional Kelvin lattices having external band gaps at low audible frequency ranges using a gradient-based design optimization method. Elastic wave propagation in an infinite periodic lattice is investigated by employing the Bloch theorem. We model the ligaments using a shear-deformable beam model obtained by consistent linearization in a geometrically exact beam theory. For a given lattice topology, we enlarge band gap sizes by controlling the configuration of the beam neutral axis and cross-section thickness that are smoothly parameterized by B-spline basis functions within the isogeometric analysis framework.